Improvement of magnetic field calculations by extrapolation

Magnetic field calculations by the boundary element method (BEM) are appropriate to particle optics simulation due to the inherent smoothness of field values, which is a consequence of the integral formulation of the problem. This allows the use of high-order and accurate ray tracing algorithms, as well as radial analytical continuation of axial data to obtain fields and potentials off axis with high accuracy in problems with radial symmetry. As shown for electrostatic field distributions in an earlier paper, magnetic field calculations can also be improved by orders of magnitude by extrapolation of a set of simulations with different numbers of boundary elements to arbitrarily fine discretisation. As examples for magnetic fields, in this paper we analyse a common magnetic lens with non-symmetric pole pieces and a lens with open magnetic circuit, which is a well-known test case in the literature. We will demonstrate how even artefacts, originating from insufficient numerical analysis or inherent difficulties of the BEM, can be suppressed by the extrapolation technique.